{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Forward Euler, continued\n", "\n", "First, revisit the simulations with large time steps. On Tuesday/Wednesday, we determined that, in order for the simulation to be constantly shrinking, that the time step should be < 1. \n", "\n", "Let's try that with our single-state degradation model. Here is copy-pasted code from Tuesday/Wednesday." ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "image/png": 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hnRTVWbTOY3FKFGpMBE5F2krIZPX60cV4F6g0jgB0zHDnFUve7K+5bA3bMivjNT00N6sjGqoxbkher2+5OvOlKKJbkQisYejeXl7MvMPKjM5JSZptXDy9tHBTKRISZWccgcMyvT4R4Y4bNvP0K2cYPnE2wIbVwOlDOma+kvUB0MPjhAlvAPrvkTr776uAnj5dr//My/60KyysocptoxA5lDTbWEa4qRQJibIzjsChDOGNd796E031ddz3q8Ml94kU1cwBg67D3rk19sZ9CYWY+ZbKvpfEUhOT5yuLmXfjOIIk5VYU6nFV6Bg7Nmmdj5jbhnEEDmUIb6xpa+KWq9fx3V8fYWJ6tuR+kaHSmHk3CVkEW0A16yUwf/2S5BgdO6/memSyOjflbILkXK2cTpbr2Lz8vm4SMkIyjsChzF7fHTs3c3Zihkeej8GicT4Hqy+D5pWVf9cR3iiSWxFLpid0gbVqesAt7Tr3IEkLpOVWpC1GQubFF+Ak1lVTZTgByn7GETiUKbzxusu72NLVGo/pIafGUDU4whunkiG8wakXQc1V9+CDRPT6FpAfhoYV5cfMu0nIvHgBpeDknhpsox8ujmrtiphiHIFDXT307Fi21yci3LGzl18dGmW/FeFiUzNTdsx8hXOeDklLpCpMk1V7s/fp6zkb4+KDbqwhbe+VxMw7tHZqPYek2MZ4Xj/Iq+40xd8xeuIIROQWEdkrIvtF5BNFPv+giORF5Bn75/dcn90pIvvsnzu9aE/VlDkv/u5Xb6KhTvhWlENJRw/obOlqjbtr27K5FbHCiZnvqiBm3o2TWzF60Nt2hUUto0VIVs2harLv3SQgmKBmRyAi9cCXgLcD/cAuESlmYd9SSl1n/3zZ/m4n8GngtcBO4NMisqbWNlVNmcIbPauaeUv/Wh546giTMxFdNK5lDhhs4Y3tsTbuBVg5HTZa31jd95OUW3FhVCdBVWsbYOdW7E1GbkW10XUObT3Q2hVr2/BiRLAT2K+UOqiUmgLuA24v87tvAx5TSo0qpU4DjwG3eNCm6qgga3LXzl5OX5jmR3tO+tyoKrGGQer1w7xanBLMSaDaiCGH7h06ByEJC6T5KmPm3WSyOkflzCFPmhQqVk4nya3MVPf9gm5FfG3DC0ewEXCvnB6xty3m3SLynIg8ICJOjFa530VE7hKRQREZzOd9WpSpYBHsDdu62bRmRXTLU1tDehqk0ph5N2XkVsSCyXNaaKcWR9C4QucgxLjXV6DSirTFSMB0SIFKhJtKEfPciqAWix8GtiilrkH3+u+p9ABKqbuVUgNKqYGenjIkF6uhAuGNujrhfQOb+Zf9I7w8EsEHpZWrfs7TwVkEi3vYZC0x826SUoLZykFzO7QX7XOVR1JyK5SqfbQI2jamzsHYEW/aFTBeOIKjgDsLY5O9rYBSakQp5QSkfxl4TbnfDZS6OvtmL8+43zuwmfo64b7dEQslnb5Yfcy8m6T0+mpdL3HI9OtF+OmJ2tsUJk4noZYecPNKWN0bf9sYO6If4NVG1znE/F7xwhHsBraLyFYRaQLuAB5y7yAi611vbwOcq/Uo8FYRWWMvEr/V3hYeFcSLr+to4c1XZvj24BGmZyO0aJbfC6jaH3xJEd6wcjpmfvWW2o6TyepchFMvetKsUFCqMl3epUhC9nmtC8UOMQ8hrdkRKKVmgI+gH+A54H6l1B4R+YyI3Gbv9lER2SMizwIfBT5of3cU+Au0M9kNfMbeFh4VCm/s2rmZU+cneTwXoUVjLxYDwSW8EfebfUjfqHU1mnsSSjCft2qLmXeTyeqEwzjnVjjBELVOo65YA6s2xNY2Grw4iFLqEeCRRdv+1PX6k8AnS3z3q8BXvWiHJ7g9+8o3Lbv7m3b0sK69hXt/dZhbrl6/7P6BYA1BfZNe3KyVTD8c/KfajxMm1jBsu6n243RdoXMRYtrrA6ovxV2MTL/Wdxg5UPvUSlhUI9xUihjnVpjM4sVU2OtrqK/jd2/YzM/25Tly+oKPDauAQsy8B36+p0/XaY+r8MaFUTh/ovYeH+gchO6Y51Z4ETHkkIRSE15Nk4Edbr1X64DEDOMIFrNyrR7mVWDcvzuwCYD7ByMSMeBFFIRD3AuMeTUH7BDjXh+g297apZOgaqWQWxFTx+gIN1VbdmQxmSzMTOiQ65hhHMFiCskh5Rv3pjWtvHF7D/fvPsxM2IvGE2dh7LC3vRyI78PPq4ghh0wWzryi6/nHES9i5h0aW2xlv5jaxulD+sFt7hXjCIpSRXLIrp29nDg7wT+9GHIFwkLMvEc9YEd4I6aLYDpmvgPaN3hzvMLUYWndisiilK3L69GDD+zpkBjbBnh3rxSmyuJ3PYwjKEZPX8XCGzdlM3SvbObesMtTe90DjrvwRi115osR417ffMy8l46gX+esTF/07phBUYtwUzGa2rT+RwxtwziCYlQxL95YX8d7Bzbxk+GTnBgLMeHIykFjqxZS8YpMn67XHrf0+ULMvIcRLau36JyEODrGWktxFyPTF9/cCmuoeuGmUsQ0t8I4gmJU2eu744bNzCn49mCIowJHkLzWmHk3cRXeOH9SRzt5NfQHO/v8ylj2+qrW5V2KOGfUehlU4ZDJwsg+rQcSI4wjKEaVwhuXdbXx+m1d3Lf7MHNzIfWea60zX4y4Tod4PU3mENNen46Z36Cj4ryi83KdsxI325iZ0g9sP2xjbgZG9nt7XJ8xjqAUVYYJ3nFDL0fPXOTn+0/50KhlGB+Bccsf44b4LYJ5vRjokMnq3IQL4SbBV4yXMfMO9Y06jDRutlGrcFMpnOsbs/LtxhGUopAcUlk46FuvWsua1kbu+1UI5am9zBp1E1fhDSun297W7e1x41hqYm7Wli712DYgnsEEfo0Wu7drHZCYXQ/jCEpRpfBGc0M973nNJh4bOkn+3OTyX/ASL7NG3YjoBcaYGbcnpbiLEccCY17HzLvp6dN6DxNnvT+2X1i52oWbitHQrEuRxOxeMY6gFDUsgr3vhl5m5hTf+XXAmcbWELR06NopXuPEi8clcmhuzg4d9XjoD7qOf3N7vG52v3rAEM/cCiun1zdqEW4qRQyzz40jKEUNwhvbMivZuaWT+371CirIB6c17F3W6GIy2YpzK0Jl7DBMnffnwVfIrYjR1FAhdNSPEVIM58X9iBhyyPTD6EswFZHaY2VgHEEpmlfVJLyx67WbOTRygV8cHPG4YSXwss58MeIWJujXQrGD0+uLywjJGtL6Ek1t3h979WU6dyUutuGVcFMpMllAxSq3wjiCpahhXvztV6+nvaWB+4LKND53AibO+GjcMZsXLyyc+1Qe2cmtOG/5c3yvsXyaJoOKlf1CxyvhplI4CXtxcYx45AhE5BYR2Ssi+0XkE0U+/5iIDNni9Y+LyGWuz2ZF5Bn756HF3w2VGoQ3Whrr+Z1Xb+KHL5xgdDyA5BLnJvRj6A+28Mb6+Bi3ldNz+S0d/hw/TiWYnZh5v2wD4hU55PdoMYa5FTU7AhGpB74EvB3oB3aJyOIr/DQwYIvXPwD8X67PLiqlrrN/biNKuIU3quCOnZuZmp3ju0EsGvsVMeQmTotgfk6TQbymykb2+xMz7yaT1Zncccit8FK4qRj1DdAdL2U/L0YEO4H9SqmDSqkp4D7gdvcOSqknlFLOysmTaJH66FNjRm3funau713NfbsP+79onM9BW8b7mHk3mX7Ivxh94Y3ZGd1OPx3Byh5o7Y7HAqmfEUMOmRhNh+SHvRNuKkWcRkh44wg2Au6J8CP2tlJ8GPhH1/sWERkUkSdF5J2lviQid9n7DebzAdW88UB4Y9cNvey3zjP4ss8KX35GQTg4uRVRF944/RLMTvrbA4b43OxOzHy3xzHzbgojpBiMGIO6V84eiU1uRaCLxSLyb4EB4POuzZcppQaA9wNfFJErin1XKXW3UmpAKTXQ0+OBulI5NLbo4WMNxv2Oa9ezsrmBe/3MNJ6b83cx0CEuvb4gpslgvuZQ1COH8sPQtU0nO/nFqvV6PSbqtuG1cFMpCiG18Qgx9sIRHAU2u95vsrctQERuBj4F3KaUKqTcKqWO2r8PAj8FrvegTd5Ro/BGa1MDt1+3gUeeP87YxcoXncti7BWYHvdfQLzbya2I+M1u5QCZb69fZPp0rsJYyBoUy+F1Ke5ixCX73LmXA+s0xWCEhDeOYDewXUS2ikgTcAewIPpHRK4H/j+0E7Bc29eISLP9uht4PRCtK+eB8Maunb1MTM/x4DM+JWP5HQXh0LwyHsIbhZj5Vn/PE4cF46kLOrnJb9uAeORW+B1d59DRC41t0bYNFzU7AqXUDPAR4FEgB9yvlNojIp8REScK6PPASuDbi8JEs8CgiDwLPAF8TikVradMJluz8MbVGzu4emM7/+OXPmUa+5k1uphMf/SHu36U4i5GIYQ0wjf7KZ9j5t1k+nUuy/mT/p+rWqxhnfy2+rLl962Fujo9Cot6p8nGk2VzpdQjwCOLtv2p6/XNJb73r8CrvGiDb7h7feuvrfowu3b28qnvvcCzR8a4bvNqb9rmYOWgYzO0tHt73GJksrD/MR2b3tDk//kqZWZSh0tmb/X/XCtW61yFKDuCoEaLsHA6ZNU6/89XDX4IN5Uik4UXf+T/eTzAZBYvR+flUNdYs2e/7doNrGis96c8dRBREA6O8MZodbkVvjOyH9RsgNcj4rkVVg7qm2HNVv/PFYdggqBGi6DXTMYtGA9Bm6RCjCNYDo+EN1a1NHLrtet56NljnJ+c8ahx6Jj5U3uDmRaC6JeaCCpiyKGnz9atiGhuhZXzP2beoa1b6z9E1TbGT/kj3FSKODhGG+MIysGjePFdO3u5MDXLQ88c86BRNqMHYXYquF5OV8SFN6whqGvwvs58KTL9Omdh9KVgzlcpQY4WIdq5FYVOQlCdphgEE9gYR1AOmawnwhvXbV5N37pV3Lfbw+khv1TJStHYEm3hDStnx8wHtH4R5RLME2M6qSlQR9BflbJfIAQVOuqwah20rI7uCMmFcQTl4JHwhohwxw2bee7IGC8cHfOgYczHzDv6CUEQ6V6fzzWGFtNzJSDRvB5WwA8+0Nc+qrkVfgo3FUMkHlF2GEdQHh7Oi7/r+k00N9Tx778+yOf+cZg9x8ZqCym1hqBzKzSuqLltZdOTrTm3whemxuH0y/NlgIOgqQ3WRDS3wu9S3MWIcglmZ6HYD+GmUjghpFHOrcA4gvJYvQUaVnji2TtaG/m7DwywY+0q/u7nB/ntv/1nbvp//om/fuxF9p08V/kBg4yCcHCEN6ImTeh3nflSOKUmooaV00lNHb3BnTOqwQR+CzeVItOvp+jOHQ/2vBUSQChBAvA4OeSNO3p4444eRsen+OELJ3j42WP815/s428f30ffulXceu0G3nHNei7rWkZNamZSl8juv33p/bzGvQi24bpgz70UQcbMu8lkYd+Popdb4ZSWCCJm3qGlA9o3Rc8xnjuuH8ihdJrQ/4v2DcGeuwKMIyiXTD/s/7Gnh+xsa+L9r+3l/a/txTo7wSPPH+f7zx3n84/u5fOP7uWaTR2845r1/PY1G9i4usjUz6l9wcbMFxpuC29EbYHUGtIx850BxMy7cXIrRvbD2oAfNEth5WDH24I/byYbQdsIMPvejXuqbFvRvNpIYBxBuWSy8Mw3YXwE2rq8P3x7Cx98/VY++PqtHD1zkR88d4zvP3ecv3xkmL98ZJjXXLaGW69Zz29ds57Mqhb9pbB6wFEV3rByevG2rj7Y87p7fVFxBOOnYDwfvG2Avh4v/UznuASRv1AOQeeXOLR1wcq1Nech+U1E/ksxoMcVJtj2Bl9PtXH1Cu564xXc9cYrOHRqnB88f5yHnz3Gnz08xJ9/f4jf2NrFrddu4F2jz7OirgE6i1bu9pdMH7zyZPDnXYr8MGzx939TlK5t0cutCKsHDPphOzupdSH81ECoBCsA4aZSxEDP2SwWl0tIWYJbutv4/Tdv44d/9EYe++M38gc3bufk2Qn+8/ee519+8XOO1G/igWctzk74VOK6FJmsDhGMivDGxTNw9mjwPT7Qdf67tkXTEYQ1IoBoPfzCWCh2cEJIo5hbYWMcQbm0b4DmcIU3tq9dxcfesoPH/+Ob+MFH38DAihMMz23if//2swz8xY/5918f5MFnjjLuZQmLUhRyKyIy5A06WWgxUas5ZA3pZKYwir91Ryy3Ym5O20eYtjF9Ac68HM75y8BMDZWLSGQSqUSEq7obYPIYN735Q3xv62/y/eeO8/3njvHY0ElaGuu4qW8tt167nn9zZYaWRh/mzN0jpM07vT9+pQShy7sUmX4YelDX//dbB6EcwoiZd2hq1Qv2EbhXAFu46UKw+RRu3FF2QQcylIlxBJWQ6YM9/1PHJIdxg7mxe8CS6ef63jVc37uGT/1WlsGXT/Pws8d45Pnj/OD547Q11fPWq9Zx67XrecO2HpoaPBoERk14w8pB00pdjjsMnNyKU3thQ8gie0rp6/Gq94TXhijlVoQ5TQbzWf/5HPT9VjhtWAbjCCoh0w9PfQ3OnYD2gNLUS1EkCqKuTti5tZOdWzv59K39PHlwlIefPcYP95zge08fpWNFI7dctY53XLue113eRUN9DU6hrk4beFSmQ6ycXpQLy0G7R0hhO4Jzx2FyLLzREej/xd5/1Lkufmoll0NQqmSlaGnXHZSoOMYieOIIROQW4G+AeuDLSqnPLfq8Gfg68BpgBHifUuqQ/dkngQ8Ds8BHlVKPetEmX3AXGIuCI2ho0ZKMRWior+MN27t5w/Zu/uKdV/PP+/N8/1k9SvjW4GG62pq45ep1bO1uo7Wpgbbmev27qZ7WZv17RVM9bU0NtDbX01Rfhyx+yGb6dSJVFLBycOXbwzv/mq06hyEKjjHsaTLn3GpW57qsuzq8dkCwwk2liMi0cilqdgQiUg98CXgLcATYLSIPLZKc/DBwWim1TUTuAP4KeJ+I9KM1jq8CNgA/FpEdSqloFnd3z/VdcWO4bbGGyo6Zb2qo48a+tdzYt5aJ6Vl+ujfPw88d4zu/PsLEdHmRDA11QmtTPW3NDQUH8d6pFXxg3OLj//AErOjS2y9xKNqRtDbq7zrHaG3S+9XXedCDP5+HC6fCG/qDjpfv2RGNm70QOhqmI3DdK1FwBGE6RdDnP/hTmJ3WGicRw4sRwU5gv1LqIICI3AfczkIR+tuBP7NfPwD8v6K7l7cD9ymlJoGXRGS/fbxfeNAu74mS8IY1DJe/qeKvtTTWc8vV67jl6nXMzinGp2a4MDnLhakZLkzNMj5p/7a3j9vbL0zNMG7vNz41y4XJGV45twWAyWN7eHI2W9h3dq78AlvNDXW0NtXbDkGoE6gTQezfoGeh6kQQ7G32Z3UCgnDdzLP8FfCpf53lucF/RkQvqOv9548nrmPU1envOtv1sbh01IPevuB9Ud8lfPjcWnbkn+Pj9wyW3K/YV4vvV72D/ID1c66q7+Tj3z0EHKr6OLXMstWraf6Gen70xBM89Nzl1R+oRurULF88uZcnJq/ie994KrR27Dy7gg/NTvHn9zzMiaba9JI/fetVrOto8ahlGi8cwUbAXXP2CPDaUvsopWZEZAzosrc/uei7G4udRETuAu4C6O0NsIjWYnr6wu/1XTwN547V3MuprxPaWxppb6myh3J2M/z1p/jim5th500AKKWYnJnj4tS8Eyk4l0nHqSx0LBemZplTijmlv68UzCmFwv5tb59TFLZh7zOnFNefOQ7jcHH1DnrqmwvfmbMrPs4pxdwcKPQxZucU07PKdQ7APv5i9B6u98X2sbfl5jbxutkfc+b0Kcbl0jpR5VaZrbVQZdeFAxyQXl46NV71MRb/3dVwuG4jHef2cWDufM3HqpbNs0doZJpnJtdzIB9eO2R2LR8C6k4Nc6CxtsoEUzPe5yPEZrFYKXU3cDfAwMBAeDVdM/3w9Dd0bHKQxbzcOOnqYQ79wRbe6FgwQhIRWhrraWmsZ01bQAXYHv4HuLCGv/5f3xpuNNfecbj3azzwO2ugd3FfKCDm5uD/PAavvpNH3/7GcNrg8O3XsOXY0/zoDysfuXrGnv8J34Y/+Xfv4k/CLJA4vRM++zH+jxsE3hzi9SiBF0+yo4A7Zm+Tva3oPiLSAHSgF43L+W60yGRhejxc4Y0oLAbCvPBG2COkMGPm3UQho/bMy3bMfMi2Afp/cvqQ1okIizCEm4rRuEIXa4zCtHIRvHAEu4HtIrJVRJrQi78PLdrnIeBO+/V7gJ8oPU5+CLhDRJpFZCuwHfiVB23yjyjokFo5aFoFHZvCa4ODk1EblvCGEzMfhQdfx2adyxC2bUC4C+cOhSi7ELPPrSH9AA5SuKkUEY4cqtkRKKVmgI8AjwI54H6l1B4R+YyI3Gbv9hWgy14M/hjwCfu7e4D70QvLPwR+P7IRQw5REN7ID2ujCrsHDC7hjRPhnP/sUZg8Gw1HUFen15DCLMFciJkPuQcMrk5TiI7AuVeiQKYfRg/A9ETYLbkET9YIlFKPAI8s2vanrtcTwHtLfPezwGe9aEcgtHRA+8bwPLtScHIPZG8N5/yLWSC8EUJuRZR6wKCvx4s/DO/8Vk5nfYcZM++wZovOdQmr0zQ9EY5wUykyfaDmYGQfrHtV2K1ZgCk6Vw1hDvHG83BxNDq9nLA1asMst1yMTFb/j87nwzl/fji8mjqLqauH7hBzK0ZCEm4qRRSmlUtgHEE1ZLJw6kUtvBE0UVkodmjr0nXew3QEK9dBa2c451+MO/s8aGantV1GxTYg3GCCqI0WO6+AusZILhgbR1ANmf554Y2giZpxQ7glmMOsM1+MMHt9owdhdip6tnHumNaLCBprSD94wxBuKkZDkxbqMSOChBBmmKCVg9YuneEcFTL9kN8bvPDG3Kw+b5QefCvXwoo14dzsURstQri6FdawFgxqCCifpRyiplthYxxBNYQpvBGVmHk3hdyKV4I97+lDMHMxWg++MHMrrBxInZ6XjwqhdpoiNloEvaZ25hWYDC/LuRjGEVRDU6uOiAjauJ2Y+agsjDqEJOM5r0oWtZvdLkMSdG6FldNVUKMQM+/QsUnnvARtG5PndXJdlEaL4FpD2htuOxZhHEG1ZPqDj48eOwJT56L54IPgHWOUYubdZLJaD+DssWDPG5XEOjciOoop8E6C/aCN2vWIQvZ5EYwjqJZMFkb2a+GNoIjiQjGEJ7xh5WB1LzSvCva8yxHGgvH0hE5WipptQDjz4lFcLwE7t2JF5BaMjSOoFrfwRlA4IYlRiRN3k8kGP0Jy1kuiRhghpKde1MlKUXvwgf4fXRgJNrciP7ykcFNo1NVHS9nPxjiCagljXtzKwaoNOiolamSyWq83qNyK2WnthKP44Gvt1LkNQdsGRNsxBvnwq0C4KXAy2XDrLxXBOIJq6doOdQ3BG3cURwOgoyFmp3QsexCMHIC56fBLcZci0xesbeRzOma+KyIx827CyD6P6mgR7NyK43BhNOyWFDCOoFoamnSMclCePYox826C7vVFdQ7YIejcCiunk5UiKIPIygys6AzONi6e1g/aKNsGRGpUYBxBLQS5CHb6EMxMRNe4e+zciqCMO4ox824yWa0LcOblYM4XxZh5Bye3IjDbcMKKTaepXIwjqIUghTcKc8ARvdmDFt6whnTpgEZvtVs9I8jIoclzOkkpqrYB84Uag8itKIQVR3QatX0jNLdHKnLIOIJacAwtiJ5O1KpsFiPIqqxRjJl34+Q2BOEYCzHzEe0Bg51bcVbrR/hNlISbiiFiJx2aqaFkEGSvzxqC1ZdB06Wi6JEhk9WLuH4Lb0xf1AX/ouwImldpXYBAbCMmnQQI7npERbipFGEr+y2iJkcgIp0i8piI7LN/XxLXKCLXicgvRGSPiDwnIu9zffY1EXlJRJ6xf66rpT2B07kV6psDNO4I9/hgPrdixOfciijHzLsJaoRk5XSSUtRi5t0ElX2uVLTXSxwy/VpX5LwVdkuA2kcEnwAeV0ptBx633y/mAvABpdRVwC3AF0Vktevz/6SUus7+eabG9gRLITnE55t9Zko/XONg3OD/kDfKMfNuMln9f5ud9vc8UY6Zd2jthFXr/beNgnBTDGwDIrNgXKsjuB24x359D/DOxTsopV5USu2zXx8DLCBCNZRrJIhKk6MHYG4m+sYdlPCGNQT1TXpxOspk+oPJrYjDaBGCibIrhBVHeJoMIqdWVqsjWKuUOm6/PgGsXWpnEdkJNAEHXJs/a08ZfUFEmpf47l0iMigig/l8SDKAxcj02cIbp/07R9Rj5h2CEt6wcjpsNIox826C6PVdGIXzJ6JvG+DKrZj17xxxGS2u7NG6ImEo2RVhWUcgIj8WkReK/CxQhFZKKaDkyoeIrAf+AfiQUsrJsvkk0AfcAHQCHy/1faXU3UqpAaXUQE9PhAYUQUyHWDmQev2QjTo9AWTUWsPRXhh16N6hcx38dIxRLcVdjJ4+rR9x+pB/57CGoifcVIowZTwXsawjUErdrJS6usjPg8BJ+wHvPOiLrnyISDvwA+BTSqknXcc+rjSTwN8DO734owIliAJjVk6XDmgoOWCKDpl+nUTll/DGxFktgBOHB19ji/+5FXEZLUIw0yFRFG4qRZC5FctQ69TQQ8Cd9us7gQcX7yAiTcD3gK8rpR5Y9JnjRAS9vvBCje0Jno7N0LQyAOOOwY0O8+085ZPwRhxi5t34XZXVyunkpPaN/p3DK5zcCr86TUrpax2ne2XqPIwdDrslNTuCzwFvEZF9wM32e0RkQES+bO/zu8AbgQ8WCRP9pog8DzwPdAP/pcb2BI+Iv2GC0xf1YmOcHnzg3/WIUw8Y9P9t1MfcijjEzDs0r9S5MH7ZhiPcFIdpQwinGF8JGmr5slJqBLipyPZB4Pfs198AvlHi+zfWcv7I0NMHwz/QPRKvb8j8XkDFx7jXbNF14H1zBDlobNUPlDjQ06dzHk69COuv8fbYTsx89jZvj+snfnaa4rJQ7OBENlk52PG2UJtiMou9wEkOGfchmiluxu238EYhZj4mpuvnvPj5kzpaLS62AbZuxYs6N8Zr4hI66rBijdYXicCIICZ3U8TxczokLjHzbvyMhsgPx+vB1+VjbkXUCxEWI9Ovc2JGDyy/b6VEWbipFGHIeBbBOAIv8LPXlx+G7iuhvqZZvGBxhDe8zq0YH9G94Dg9+OobdRipH4UJ4zZaBH87TfkYBVU4ZLL+51aUgXEEXuCn8EacIoYc/MqtyMewBwz+9fqsIWjt1slJcaFru86J8doRFISbYmgbs5Mw+lKozTCOwAv8ihyaOKtDy+Iy5+ngV4GxQpXNuN3sfVovYPKct8eNYyfBr9yKqAs3lSKIPKQyMI7AKxxBai+TQwpZozEa+oOuA9+0ynvHaA1Bcwe0b/D2uH5TkCb0MLdCKXu9JGYPPvCn0xS3sGKHHlfkUIgYR+AVfghvxNW4/RohOclCcYiZd+NHzaGxwzoZKW62AXZuxUGdI+MVcdBkKEZTmw65DnnB2DgCr/BjwdgahsY2LXASN7wW3ohLnflirN6i9QK8XDOJ40KxQyYLKB1G6hVWTj9QoyzcVIoI1BwyjsAr/JgXt4b0/HJcYubdeJ1bce4ETJyJ54Ovrk7/H722DYhfDxh86jTl4rd25NDTByP7/cmtKJMYPmEiSmsnrFxnjNsh47FjjFuy0GJ6PJ4qK8TMr/bumEHRebnOjfHKNuIi3FQKJ7diZH9oTTCOwEu8DBMcPwXjVryNG7x7+MV5KgT0//H8Ca0f4AVxnSYDnRPTvcM72xjZHw/hplJEQK3MOAIvyfRD/kVvkkPimDXqps0W3vDKuPM5fcy2bm+OFzReOsa5WW1ncbUN8DaYIK5BFQ7dPuVWVIBxBF6SyXonvBHX0FEHEXsRzKMF0jjGzLvxMl589CWdhBRX2wB9PcYO61yZWskPx0e4qRgNzdC1zTiCxOBlr88agpbVsGpd7ccKC6+EN+bm7NDRGD/42jfoHAivbANi7hg9zK2Ik3BTKbwOJqgQ4wi8xBHe8ORmj1Gd+VL09On68GNHajvO2CswPR7PCBkHEftm98g2YN7e4oiXUXZxXi9xyPTrmYSpC6GcviZHICKdIvKYiOyzfxct+ycisy5Rmodc27eKyC9FZL+IfMtWM4svzSthdW/txh3nmHk3Xo2Q4r5Q7OBVboU1FN+YeYfVl2ldiVptY+qCnipLgm2g/FP2W4ZaRwSfAB5XSm0HHrffF+OiUuo6+8etovFXwBeUUtuA08CHa2xP+GT6a680ee44TIwlwLg96vUVHEGMRwRg51ac1hVUayFupbiLUVenRwW12sYpW7jJdJpqolZHcDtwj/36HrTucFnYOsU3Ao6OcUXfjyxeCG/EPWLIwRHeqNUxWjlo3wQtHd60Kyy8KME8M6nDJeNuG+BNp8mKeVCFw5qtUN8c2jpBrY5grVLquP36BLC2xH4tIjIoIk+KyDvtbV3AGaXUjP3+CFBSgVtE7rKPMZjP+6AE5hVeCG/EtcpmMbzIrYh7xJCDF72+uMfMu8lk9ehofKT6YzjCTWu2eteuMCjkVvigW1EGyzoCEfmxiLxQ5Od2935KKQWUmvy8TCk1ALwf+KKIXFFpQ5VSdyulBpRSAz09Ea6/7sUimJWDtgy0dXnTpjCpVXhjdkYP/+M+LQQ6B6K1u3bbgHgvnDs4/9NaQmqtXPyEm0rhp57zMizrCJRSNyulri7y8yBwUkTWA9i/rRLHOGr/Pgj8FLgeGAFWi4jzH9wEeFi6MyS6d4DU1fYPTcJCsUMmq+vEV5tbMXoQZqeS0QOG2m92ayjeMfNuvBghJWW0CPrvOHtErw8GTK1TQw8Bd9qv7wQeXLyDiKwRkWb7dTfwemDIHkE8Abxnqe/HjsYW6LyieuOem0vGYqBDrenzcVUlK4UzL15t5JA1rJOP4hwz77BqvV73qdY2Jsb0gzNJtgGhTA/V6gg+B7xFRPYBN9vvEZEBEfmyvU8WGBSRZ9EP/s8ppZz//MeBj4nIfvSawVdqbE80qKXXN/YKTF9IjnEXpsqqNG4rB4ge/ieBTFbrCIwdru77SRot1pp97iSjmU5TzdQ0saaUGgFuKrJ9EPg9+/W/Aq8q8f2DwM5a2hBJMv2Qe1gLbzSuqOy7SYmZd6hVeMMags6t0NTqabNCwz0dsrpCnYmpcT3Fdu0uz5sVGpksvPBdPUKqNHky7hVpF9OxWeuP1BpJVQUms9gPMn2Aqi59vlBnPiE9YKitBHOcS3EXo5B9XoVjzDsx8wl58IH+306c0XoTlWLl4ivcVAw/dCvKPXXgZ0wDtSyCWTndM2hp97ZNYZLJ6nrxleZWzEzCyIHkTIWA1g9o31i9bUByRotQ23RInIWbShFS5FCCrmCEcIQ3qgmLS1IUhEO1whun9oGaTeD1qDK3Ip/TSUdxj5l3U0uSXVLvlfE8nA82V8o4Aj+ob6xOeGN2RmclJ864qyzBnMQeMNi5FVXoVlg56NmRjJh5h7ZunTNTqW2Mn9IPzCTaBnhTrrwCjCPwi2qGeEmLmXeoVnjDGoK6Bh0umSQy/VpPYPSlyr5n5ZJnG1DdvZKkxDo3znpYwCGkxhH4RU9f5cIbcRYkX4qGZl0vvpqbvWsbNMS7KO0lVJN9fvEMnD2aPNsA2xEM6xyacknqaHHVOq1DEvCCsXEEflEQ3qjAszsx80mKGHKoZl48STHzbnquBKQyxxh3xbqlyGS13sTYK+V/JwnCTcUo5FaYqaFkUM0imDWkF5orzT2IA5l+PRVSrvDG1DiceTmZD75qciuSUpG2GNVE2TnTZHEWbiqFV8p+FWAcgV9UI7yRH07mjQ4u4Y0Xy9u/0ANO6vWosASzlYOmlTq0OGkUpsrKvFeU0oupibWNLEyOwdljgZ3SOAK/qFR4Y3rCjplPYA8YKu/1JXUO2CGT1eG0M5Pl7W8NaXtKUsy8Q0u7dnDl2kZBuCnBjgACjRxKoFVFiEqiIUacmPkELgaCLbzRVL5jtHLQ0KKnUJJIJltZboWVS65tgN1pKreT4JSWSKgj6Kkht6JKjCPwk0wWxq3yhDeS3gOub9CF4yq52bt3QF29v+0Ki0rWkM7n4cKp5NoG2Mp+e3UuzXIkSbipGG1dsHKtcQSJoZIhnpWDukZdwjqpZLLlz4tbCSrFXYyu7TpHopybPWmluIuR6dc5NKfLyK2whvWDMgnCTaXwQtmvAowj8JNK5sWtnE68SlrMvJtMtrzcioun4dyxZD/4Gpp0jkS5tgHJdoyV1BxKalixmx5H2a+C3IoaMI7AT1ath+YyhTfSYNzl5lYkRZB8Ocrt9VlDsGKN7gUnlXJzKxzhpqROCzlkslqX5MzLgZzOOAI/ESlvwXjyvP6HJ964y8yoTVqd+VL0ZLW+wNT40vs5pbiTGDPv0LhC604sZxtnXk6WcFMpvJDxrICaHIGIdIrIYyKyz/69psg+bxaRZ1w/EyLyTvuzr4nIS67PrqulPZHE6fUtlRxSUFpKuHF39Or68csZd5Jj5t04uRVL6VYolcwqm8UoJ6M2DdNkUJtuRRXUOiL4BPC4Umo78Lj9fgFKqSeUUtcppa4DbgQuAD9y7fKfnM+VUs/U2J7okenXMc9LCW+kYTEQXMIby9zsTmJdknvAUN5U2dljMHk2+bYBdm7FgaVzK5x7JYllWNy0tOuOUxxGBMDtwD3263uAdy6z/3uAf1RKlVlnIAGUswhm5aBhRXJj5t0sN1WmFJzck44HX+dWrS+wnG1A8nvAoP/nalbrUJTCyukHZJKEm0pRTqfJI2p1BGuVUsft1yeA5Vaz7gDuXbTtsyLynIh8QUSaS31RRO4SkUERGczngxVtqIly4sWtId3DSWrMvJtMv51bcar45+N5uDiajgdfXb3+vy9nG5AOx1jOvHjSE+vcOMp+s9O+n2pZRyAiPxaRF4r83O7eTymlgJIT4SKyHi1i/6hr8yeBPuAGoBP4eKnvK6XuVkoNKKUGenp6lmt2dGjrhraeMow7BTc6LF9XJqmluEux3AjJyuloodbO4NoUFp1X2LkVJUZIs9PJFG4qhZNbMXrQ91Mt6wiUUjcrpa4u8vMgcNJ+wDsPemuJQ/0u8D2lVMG9KaWOK80k8PfAztr+nIiyVJjgxdO6dkqajBuWcAQpmgoB/X8/e1TrDRQjDWHFDg1NOtGulG0kVbipFLXoOVdIrVNDDwF32q/vBB5cYt9dLJoWcjkRQa8vvFBje6JJpr90ckhaYuYdHOGNUtnWVg5WdMLKTKDNCo3CgnGRyKG5Ob09LbYBdvb5cp2ElDjG7h0gdYGsE9TqCD4HvEVE9gE32+8RkQER+bKzk4hsATYD/7To+98UkeeB54Fu4L/U2J5ospTwRprmgGF54Y0k15kvxlK9vjOHYOZiemwD9P++VG6FldMPxu4dgTcrFBpX6GKNAYwIalLBVkqNADcV2T4I/J7r/SFgY5H9bqzl/LHBXU1wcWSQlYPmdmi/5PIkl0wfvPAdHSHkfuA7MfPXvi+8tgVNx2adM1HMMSa9uFoxnIXg/DBsfM3Cz6wh/WBMonBTKRwZT58xmcVBsFRGrZXTC6Np6QGDK7fi+MLtY0dg6ly6esAipXUrCgvnCY+Zd7PUGlKagiocMv0wekDrlfiIcQRB0NIB7ZsuNW6l0rUY6FBqOiRtC8UOpSKH0hQz77Bmi9ahWHw9pif0AzGNtqHmylf2qxLjCIKi2BAvTTHzbgpTZYuuRyFrNCWhow6Zfq03cH5RfoyVYOnSUpTKrRjZpx+IabseAdUcMo4gKIoJb6RtodihlPCGldMVW9MQM++mmG5F2mLm3RQLJkjraLHrCq1T4vOCsXEEQZHJXpockrZwODfF5sUdXd60USz7fOQAzE2n1zbOHdM5Ng7WkH4gdiVYuKkY9Y1ap6RcQacqMY4gKIrNi1tD0NqlM4/TRqZfG7eTWzE3m76YeYeVa7XewGLbgHQ6gsJ0iOvh5wg31TeG06YwCUCtzDiCoOguIryRtph5N4uFN04fgpmJdD74iuVWpC1m3k2pTlMabQP0333mFZg859spjCMIiqZWXW3SmQdWKp2LgQ6LSzCndQ7YwQkmcHQr8jnovDxdMfMOHZugadW8bUye1w/C1N8rS+hW1IhxBEHi7vWlMWbezWLhjULyVIpi5t1ksjA5pvUHIJ0x8w6Llf0Kwk0p7ST0LJGH5BHGEQRJT59eBJyeSGfWqJuWdp1V61wHawhW90LzynDbFRbu7PPpizqoIK22AToJ8+Se+VwbSGcgAdi5FSt8zTA2jiBIHOGNkX3p0eVdCnevz1kvSSvuefFTL6YzZt5Npl/n2Izn0yXcVIxCboUZESQDd3KIlYNVG3S0SFrJZPVDb/qido5pfvC1dsLKdfO2AcYxgn74pUm4qRTl6DnXgHEEQdK1zRbeyOnFwDQ/+GBeeGPfj2BuJt0PPpgvwWzl0hkz78YdQpofNraRycL5E3Bh1JfDG0cQJI7wxskX7Jj5tDsC++9/4TsL36eVTL9+8J3co8NG0xgz79DWo3NsXv6XdAk3laIcydsaMI4gaDJ98NLP0hsz78YR3njxUf27a3vYLQqXTJ/WHzj083SvHYFdlTWrR4tg7pViZUg8xDiCoMn0aycAxrgd4Y2ZCa1X29gSdovCxZn+MJ0ETSZr7hWH9o1atySKIwIRea+I7BGROREZWGK/W0Rkr4jsF5FPuLZvFZFf2tu/JSJNtbQnFrgNOq3hcG6c65H2Gx0W5lCkfU4c5m0ibcJNxVicW+ExtY4IXgB+B/hZqR1EpB74EvB2oB/YJSKOlf8V8AWl1DbgNPDhGtsTfZwbfM0WaGoLtSmRwLke5sEHzat0LgUYxwgu28imswzLYpxCjU72uYfU5AiUUjml1HJ5zzuB/Uqpg0qpKeA+4HZbsP5G4AF7v3vQAvbJxhHeMA8+jRkRLCTTr2PmV28JuyXh46yTGNvQZPp1RdbzJz0/dE2axWWyETjsen8EeC3QBZxRSs24tpcc/4nIXcBdAL29vf60NAjq6uFtf5neUgqL2f4WeN1HYNsl0tfp5Df/ALa/FerM8h0r1sDNfw5XvDnslkSDTQNw1bvm1008ZFlHICI/BtYV+ehTSqkHPW9RCZRSdwN3AwwMDHg/NgqSG5I/A1Y2zavgbZ8NuxXRYcsb9I9B84Y/CrsF0WHTALz3a74cellHoJS6ucZzHAU2u95vsreNAKtFpMEeFTjbDQaDwRAgQYw/dwPb7QihJuAO4CGllAKeAN5j73cnENgIw2AwGAyaWsNH3yUiR4DXAT8QkUft7RtE5BEAu7f/EeBRIAfcr5TaYx/i48DHRGQ/es3gK7W0x2AwGAyVI8qHUCS/GRgYUIODg2E3w2AwGGKFiDyllLok58uEJhgMBkPKMY7AYDAYUo5xBAaDwZByjCMwGAyGlBPLxWIRyQMvV/n1buCUh82JO+Z6zGOuxULM9VhIEq7HZUqpnsUbY+kIakFEBoutmqcVcz3mMddiIeZ6LCTJ18NMDRkMBkPKMY7AYDAYUk4aHcHdYTcgYpjrMY+5Fgsx12Mhib0eqVsjMBgMBsNC0jgiMBgMBoML4wgMBoMh5aTKEYjILSKyV0T2i8gnwm5PWIjIZhF5QkSGRGSPiPxh2G2KAiJSLyJPi8j3w25L2IjIahF5QESGRSQnIq8Lu01hISJ/bN8nL4jIvSLSEnabvCY1jkBE6oEvAW8H+oFdIpJW4eAZ4D8qpfqB3wB+P8XXws0fokulG+BvgB8qpfqAa0npdRGRjcBHgQGl1NVAPVpTJVGkxhEAO4H9SqmDSqkp4D7g9pDbFApKqeNKqV/br8+hb/KSetFpQEQ2Ab8NfDnstoSNiHQAb8TWB1FKTSmlzoTaqHBpAFaISAPQChwLuT2ekyZHsBE47Hp/hJQ//ABEZAtwPfDLkJsSNl8E/gSYC7kdUWArkAf+3p4q+7KItIXdqDBQSh0F/m/gFeA4MKaU+lG4rfKeNDkCwyJEZCXwHeCPlFJnw25PWIjIOwBLKfVU2G2JCA3Aq4H/ppS6HhgHUrmmJiJr0DMHW4ENQJuI/NtwW+U9aXIER4HNrveb7G2pREQa0U7gm0qp74bdnpB5PXCbiBxCTxneKCLfCLdJoXIEOKKUckaJD6AdQxq5GXhJKZVXSk0D3wV+M+Q2eU6aHMFuYLuIbBWRJvSCz0MhtykURETQ8785pdRfh92esFFKfVIptUkptQVtFz9RSiWu11cuSqkTwGERudLedBMwFGKTwuQV4DdEpNW+b24igQvnDWE3ICiUUjMi8hHgUfTK/1eVUntCblZYvB74d8DzIvKMve0/K6UeCa9JhojxB8A37U7TQeBDIbcnFJRSvxSRB4Bfo6PtniaBpSZMiQmDwWBIOWmaGjIYDAZDEYwjMBgMhpRjHIHBYDCkHOMIDAaDIeUYR2AwGAwpxzgCg8FgSDnGERgMBkPK+f8BwaSPXwFUoZ4AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Run the 1D model to see where the steps break down..\n", "import numpy as np\n", "import scipy.integrate\n", "\n", "def degradation_model1D( t, y, params ):\n", " dydt = -params[0] * y;\n", " return dydt\n", "\n", "def forwardEuler1D( fn, t, y0, params ):\n", " \"\"\" [t,y] = forwardEuler1D( fn, t, y0, params )\n", " Given a function handle fn for dydt, find the value of\n", " y at timepoints t, given y(0) = y0.\n", " fn takes t, y, and params as input.\n", " t is 1-dimensional (NT,)\n", " y is 2-dimensional (1,NT) (NOTE WE ASSUME WE HAVE JUST ONE VARIABLE)\n", " \"\"\"\n", " y = np.zeros( (1,t.size) )\n", " y[0,0] = y0;\n", " for i in range(1,t.size):\n", " h = t[i]-t[i-1];\n", " yprime = fn(t[i-1],y[0,i-1],params);\n", " y[0,i] = y[0,i-1] + h*yprime;\n", " \n", " return (t,y)\n", "\n", "dt = 1\n", "y0 = 1\n", "params = (2,)\n", "t = np.arange(0,10,dt)\n", "tru_y = np.exp( -params[0]*t)\n", "(t,y) = forwardEuler1D( degradation_model1D, t, y0=y0, params=params)\n", "\n", "plt.plot(t, tru_y)\n", "plt.plot(t, y.T);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rewrite the forward Euler method to work for multi-state models\n", "\n", "Rewrite the method so that y0 can have more than one value and fn can return a vector of more than one value.\n", "\n", "The return value should be NY x NT (number of states by number of time steps) big, so it gets filled in one column at a time. Adjust the 1D code to account for multiple states." ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "def forwardEuler( fn, t, y0, params ):\n", " \"\"\" [t,y] = forwardEuler( fn, t, y0, params )\n", " Given a function handle fn for dydt, find the value of\n", " y at timepoints t, given y(0) = y0.\n", " fn takes t, y, and params as input.\n", " t is 1-dimensional (NT,)\n", " y is 2-dimensional (NY,NT)\n", " \"\"\"\n", " y = np.zeros( (y0.size,t.size) )\n", " y[:,0] = y0;\n", " for i in range(1,t.size):\n", " h = t[i]-t[i-1];\n", " yprime = fn(t[i-1],y[:,i-1],params);\n", " y[:,i] = y[:,i-1] + h*yprime;\n", " \n", " return (t,y)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, make a 2-state degradation model." ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [], "source": [ "def degradation_model( t, y, params ):\n", " y1 = y[0]\n", " y2 = y[1]\n", " dydt = np.zeros( (2,) )\n", " dydt[0] = -params[0] * y1\n", " dydt[1] = -params[1] * y2\n", " return dydt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run the 2-state degradation model with forward Euler.\n", "\n", "Use 2 and 2.5 as the degradation rates. Simulate from t=0 to t=4 with a time step size of 0.1.\n", "\n", "Then plot the true solution and the approximate solution (indicate simulated with dashed lines). And in another plot, show the difference (between the true and approximate solutions) over time." ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "params = np.array([2,2.5])\n", "y0 = np.array([1,1])\n", "(t,y) = forwardEuler( degradation_model, np.arange(0,4,0.1), y0, params)\n", "tru_y1 = y0[0]*np.exp(-params[0]*t)\n", "tru_y2 = y0[1]*np.exp(-params[1]*t)\n", "\n", "plt.subplot(2, 1, 1)\n", "plt.plot( t, tru_y1)\n", "plt.plot( t, tru_y2 )\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( t, y.T, '--' );\n", "plt.legend(['True y1','True y2','Approximate y1','Approximate y2']);\n", "\n", "plt.subplot( 2, 1, 2 )\n", "plt.plot( t, tru_y1 - y[0,:])\n", "plt.plot( t, tru_y2 - y[1,:]);\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Determine how the error depends on the step size\n", "\n", "When we compute the difference between the true and approximate solutions, we have one value at each state for each time step. I would like to summarize this as one number, so that we can plot \"error\" versus step size.\n", "\n", "Let's explore different measures for the error." ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-norm across states, then mean across time 0.025902904858696563\n", "2-norm across states, then mean across time 0.018549186024476992\n", "inf-norm across states, then mean across time 0.01460706848790066\n", "1-norm across states, then max across time 0.09120215528866388\n", "2-norm across states, then max across time 0.0650221500659531\n", "inf-norm across states, then max across time 0.051473191171442334\n" ] } ], "source": [ "import scipy.linalg\n", "\n", "tru_y = np.vstack( (tru_y1,tru_y2))\n", "d = tru_y - y\n", "print( \"1-norm across states, then mean across time\", np.mean(scipy.linalg.norm( d, ord=1, axis=0 )) )\n", "print( \"2-norm across states, then mean across time\", np.mean(scipy.linalg.norm( d, ord=2, axis=0 )) )\n", "print( \"inf-norm across states, then mean across time\", np.mean(scipy.linalg.norm( d, ord=np.inf, axis=0 )) )\n", "print( \"1-norm across states, then max across time\", np.max(scipy.linalg.norm( d, ord=1, axis=0 )) )\n", "print( \"2-norm across states, then max across time\", np.max(scipy.linalg.norm( d, ord=2, axis=0 )) )\n", "print( \"inf-norm across states, then max across time\", np.max(scipy.linalg.norm( d, ord=np.inf, axis=0 )) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Determine how the error changes with the time step. Plot two figures - one with the simulations and one with the errors. Compute the error using two methods:\n", "- Compute the Euclidean distance between the true solution and the approximate solution (2-norm of the difference) at each time point, then take the mean across time.\n", "- Compute the infinity norm (max value) of the difference between the true solution and the approximate solution at each time point, then take the mean across time.\n", "\n", "Make an array of time steps. For each time step, plot each solution in a separate subfigure, and keep track of the error in an array. Then plot the errors in a second figure, with each error computation in a separate subfigure." ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# range from smallest timestep that doesn't take way too long to run to largest time step with qualitatively correct answer.\n", "dts = np.linspace(1e-4,1e-1,10)\n", "err1 = np.zeros( (dts.size,) )\n", "err2 = np.zeros( (dts.size,) )\n", "params = (2,2.5)\n", "y0 = np.array((1,1))\n", "\n", "for i in range(dts.size):\n", " t = np.arange(0,4,dts[i])\n", " sol = scipy.integrate.solve_ivp(fun=degradation_model, t_span=(0,150), y0=y0, method='LSODA', rtol=1e-8, atol=1e-8, t_eval=t, args=[params] )\n", " (t,y) = forwardEuler( degradation_model, t, y0, params)\n", " plt.subplot( dts.size, 1, i+1 )\n", " plt.plot( t, sol.y.T )\n", " plt.plot( t, y.T, '--')\n", " err1[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", " err2[i] = np.mean(scipy.linalg.norm( sol.y-y, np.inf, axis=0) )\n", " \n", "plt.figure()\n", "plt.subplot(2,1,1)\n", "plt.plot( dts, err1, '.-' );\n", "plt.subplot(2,1,2)\n", "plt.plot( dts, err2, '.-' );\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bonus Content\n", "\n", "Here, we use Forward Euler to solve the Goodwin oscillator (coded up in Lecture 8). This code is hear as an example to follow when working on Project 3. Aside from being more interesting than the degradation model, the most important difference is that we don't have an analytical solution. So, we use solve_ivp's LSODA method with really tight error controls (i.e. we allow only tiny little errors) to generate the reference \"true\" solution." ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [], "source": [ "# Here is the model, copied from a notebook from earlier in the course\n", "def goodwin_oscillator( t, statevars, params ):\n", " X = statevars[0];\n", " Y = statevars[1];\n", " Z = statevars[2];\n", " alpha_1 = params[0]\n", " K = params[1]\n", " n = params[2]\n", " gamma_1 = params[3]\n", " alpha_2 = params[4]\n", " gamma_2 = params[5]\n", " alpha_3 = params[6]\n", " gamma_3 = params[7]\n", " \n", " dydt = np.zeros( (3,) )\n", " dydt[0] = alpha_1*K**n/(K**n+Z**n) - gamma_1*X\n", " dydt[1] = alpha_2*X - gamma_2*Y;\n", " dydt[2] = alpha_3*Y - gamma_3*Z;\n", "\n", " return dydt" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Simulate the model for a given time step size.\n", "# SRT reran this many times, adjusting the time step.\n", "import scipy.integrate\n", "\n", "alpha_1 = 1\n", "K = 0.61\n", "n = 11\n", "gamma_1 = 0.15\n", "alpha_2 = 1\n", "gamma_2 = 0.15\n", "alpha_3 = 1\n", "gamma_3 = 0.25\n", "\n", "params = (alpha_1,K,n,gamma_1,alpha_2,gamma_2,alpha_3,gamma_3)\n", "\n", "# Find a point on the limit cycle and start all subsequent simulations from that point.\n", "sol = scipy.integrate.solve_ivp(fun=goodwin_oscillator, t_span=(0,300), y0=(.1,.1,.1), method='LSODA', rtol=1e-8, atol=1e-8, args=[params] )\n", "y0 = sol.y[:,-1]\n", "\n", "# Run this with a time step of 0.1 (which is the biggest that looks like it is still qualitatively correct)\n", "# Run this with a smaller time step - the smallest you are willing to wait for, as well. \n", "t = np.arange(0,150,.1)\n", "sol = scipy.integrate.solve_ivp(fun=goodwin_oscillator, t_span=(0,150), y0=y0, method='LSODA', rtol=1e-8, atol=1e-8, t_eval=t, args=[params] )\n", "(t,y) = forwardEuler( goodwin_oscillator, t, y0, params)\n", "\n", "plt.plot( sol.t, sol.y.T );\n", "plt.plot( t, y.T, ':' );" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Determine how the error changes with the time step. Since we don't know exactly what the region of absolute stability is, we want to make sure we plot every solution (and not just the error we compute from it). So plot each solution in one figure, but keep track of the error in an array. Then plot the error in a second figure. Here, I compute the error by first computing the Euclidean distance between the true solution and the approximate solution at each time point, then take the mean across time." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Determine how the error changes with the time step.\n", "# range from smallest timestep that doesn't take way too long to run to largest time step with qualitatively correct answer.\n", "dts = np.linspace(1e-4,1e-1,10)\n", "err = np.zeros( (dts.size,) )\n", "\n", "for i in range(dts.size):\n", " t = np.arange(0,150,dts[i])\n", " sol = scipy.integrate.solve_ivp(fun=goodwin_oscillator, t_span=(0,150), y0=y0, method='LSODA', rtol=1e-8, atol=1e-8, t_eval=t, args=[params] )\n", " (t,y) = forwardEuler( goodwin_oscillator, t, y0, params)\n", " plt.subplot( dts.size, 1, i+1 )\n", " plt.plot( t, sol.y.T )\n", " plt.plot( t, y.T, '--')\n", " err[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", " \n", "plt.figure()\n", "plt.plot( dts, err, '.-' );" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }